It is well known that, so far there has been only one species of ac electric transformer, i.e. the conventional voltage/current transformer, the prior art of this invention as well, being widely-used in electrical engineering. As a matter of fact, it is a mutual inductor, i.e. Tr in FIG. 1(a), with its coupling coefficient k less than but close to 1. In order to address this issue more clearly, for the time being, let's review its electric characteristic equations when neglecting power loss. If the port variables of a mutual inductor supposed as corresponding to those illustrated in FIG. 1(a), in electrical theory, its electrical characteristic equations in a sinusoidal steady-state circuit are presented as
                    {                                                                              V                  1                                =                                                      jω                    ⁢                                                                                  ⁢                                          L                      1                                        ⁢                                                                                  ⁢                                          I                      1                                                        -                                      jω                    ⁢                                                                                  ⁢                    M                    ⁢                                                                                  ⁢                                          I                      2                                                                                                                                                                V                  2                                =                                                      jω                    ⁢                                                                                  ⁢                    M                    ⁢                                                                                  ⁢                                          I                      1                                                        -                                      jω                    ⁢                                                                                  ⁢                                          L                      2                                        ⁢                                                                                  ⁢                                          I                      2                                                                                                                                                                  (              1              )                                                                          (              2              )                                          where L1 and L2 respectively represent self-inductances of the primary winding and the secondary winding of the mutual inductor, M is the mutual inductance between them both; ω=2πf. And attention must be paid to its coupling coefficient k and turns ratio n, which are defined as
                    k        =                  M                                                    L                1                            ⁢                              L                2                                                                        (        3        )                                n        =                                            N              1                                      N              2                                =                                                    L                1                                            L                2                                                                        (        4        )            Obviously, the mutual inductor in FIG. 1(a) has an equivalent circuit schematically as in FIG. 1(b) [Note: FIG. 1(c) is also an equivalent circuit.], with its equations accordingly could be transformed as follows:
                    {                                                                                                                                                V                        a                                            =                                                                                                    V                            1                                                    -                                                                                    jω                              ⁡                                                              (                                                                  1                                  -                                  k                                                                )                                                                                      ⁢                                                          L                              1                                                        ⁢                                                          I                              1                                                                                                      =                                                                              jω                            ⁢                                                                                                                  ⁢                                                          kL                              1                                                        ⁢                                                          I                              1                                                                                -                                                                                                                                                                                                        jω                        ⁢                                                                                                  ⁢                        k                        ⁢                                                                                                            L                              1                                                        ⁢                                                          L                              2                                                                                                      ⁢                                                  I                          2                                                                    =                                                                                                    L                            1                                                                          ⁢                                                  (                                                                                    jω                              ⁢                                                                                                                          ⁢                              k                              ⁢                                                                                                L                                  1                                                                                            ⁢                                                              I                                1                                                                                      -                                                          jω                              ⁢                                                                                                                          ⁢                              k                              ⁢                                                                                                L                                  2                                                                                            ⁢                                                              I                                2                                                                                                              )                                                                                                                                                                                                                                              ⁢                                                      V                    b                                    =                                                                                    V                        2                                            +                                                                        jω                          ⁡                                                      (                                                          1                              -                              k                                                        )                                                                          ⁢                                                  L                          2                                                ⁢                                                  I                          2                                                                                      =                                                                  jω                        ⁢                                                                                                  ⁢                        k                        ⁢                                                                                                  ⁢                                                                                                            L                              1                                                        ⁢                                                          L                              2                                                                                                      ⁢                                                  I                          1                                                                    -                                                                                                                                                                jω                  ⁢                                                                          ⁢                                      kL                    2                                    ⁢                                      I                    2                                                  =                                                                            L                      2                                                        ⁢                                      (                                                                  jω                        ⁢                                                                                                  ⁢                        k                        ⁢                                                                              L                            1                                                                          ⁢                                                  I                          1                                                                    -                                              jω                        ⁢                                                                                                  ⁢                        k                        ⁢                                                                              L                            2                                                                          ⁢                                                  I                          2                                                                                      )                                                                                                                                              (              5              )                                                                                                                                                                                                                                                                                                                              (                    6                    )                                                                                                                        I          1                =                                                            V                a                                            jω                ⁢                                                                  ⁢                                  kL                  1                                                      +                                                                                L                    2                                                        L                    1                                                              ⁢                              I                2                                              =                                                                      V                  a                                                  jω                  ⁢                                                                          ⁢                                      kL                    1                                                              +                                                1                  n                                ⁢                                  I                  2                                                      =                                          I                0                            +                                                1                  n                                ⁢                                  I                  2                                                                                        (        7        )            In FIG. 1(b), enclosed in the broken-line box is an ideal transformer that has the simplest voltage and current relationships between ports as Va/Vb=n, I1′/I2=N2/N1=1/n. Unfortunately for a practical transformer or mutual inductor, from FIG. 1(b) or equations above, it is easier understood that its voltage ratio is
                              V          1                          V          2                    ≠                        V          a                          V          b                      =                            N          1                          N          2                    =      n        ,and its current ratio is
            I      1        =                            I          0                +                              1            n                    ⁢                      I            2                              ≠                        1          n                ⁢                  I          2                      ,            (                        I          0                ≠        0            )        .  This means that the conventional transformers, used either as a current transformer or as a voltage transformer or even as a power transformer, actually are all not precise in transformation of a current or of a voltage, as well as produce some inductive reactance capacity when transferring power since a conventional transformer or mutual inductor is both inductive and less-than-unity coupled, which is why errors exist in it inherently, due to the deficiency in its structure. Part of the errors originate from its leakage inductances (1−k)L1 and (1−k)L2 as well as magnetization inductance kL1, so as called reactance error, or more exactly inductive reactance error [Note: Reactive error not only worsens the transforming precision but also produces reactive current of the supply so as to cause more power loss and higher cost for transmission line materials]. In addition, there exist the power-dissipation error, or resistance error, from its copper loss and iron loss; as well as non-linearity error from its non-linear performance of cores. Therefore, to obtain its required precision, the conventional transformer had to resort to lots of methods for improvements while designed.
Furthermore, in a power system, due to the varieties and complexity of the network loads, there disperse great numbers of high-order harmonics in the supply network. The high-order harmonics not only contribute to energy wastes but also endanger the safety of facilities and loads, causing misoperations and mishaps, and seriously interfering with signal transmissions. The conventional transformer is powerless against those harmonics except for its insulations being threatened and cores overheated. It would have been a dream that, provided that only a few of passive components are added, it could come true that the conventional transformer will become one both transferring power from input to output and also functioning as harmonics isolation from in between, i.e. a function of waveform conversion from square-wave to quasi-sine being added. It was just a matter of regret, being long expected but not realized yet, in the past.